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Convergence results of forward–backward method for a zero of the sum of maximally monotone mappings in Banach spaces

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Abstract

The purpose of this paper is to study a forward–backward algorithm for approximating a zero of the sum of maximally monotone mappings in the setting of Banach spaces. Under some mild conditions, we prove a new strong convergence theorem for the algorithm produced by the method in real reflexive Banach spaces. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example, which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.

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Acknowledgements

The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions.

Funding

The authors gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST).

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Authors and Affiliations

  1. Department of Mathematics and Statistical Sciences, Botswana International University of Science and Technology, Pvt., Bag 0016, Palapye, Botswana

    Getahun Bekele Wega & Habtu Zegeye

Authors
  1. Getahun Bekele Wega
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  2. Habtu Zegeye
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Correspondence to Habtu Zegeye.

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Communicated by Carlos Conca.

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Wega, G.B., Zegeye, H. Convergence results of forward–backward method for a zero of the sum of maximally monotone mappings in Banach spaces. Comp. Appl. Math. 39, 223 (2020). https://doi.org/10.1007/s40314-020-01246-z

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  • DOI: https://doi.org/10.1007/s40314-020-01246-z

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